An analytical-based computational framework to study poroelastic column consolidation for solid compressibility at large deformations

Abstract

This paper presents a computational framework based on a semi-analytical solution to predict the time-dependent behavior of fluid-saturated poroelastic media. The proposed method (PM) employs the Forward Euler Method to approximate time derivatives in the fluid continuity equation, transforming the governing partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). These ODEs are then solved analytically to determine pore pressure and skeleton deformation at each iteration. A one-dimensional column consolidation with a compressible isotropic-homogeneous porous skeleton is used as a case study. The skeleton’s large deformations are described using the Hencky material model, incorporating a decoupled porosity-deformation-dependent free energy function. The accuracy of the results is validated against simulations performed using the FlexPDE commercial software, showing excellent agreement in predicting consolidation behavior and confirming the reliability of the method. By avoiding spatial discretization and variable conversion, the PM achieves rapid and efficient convergence. Furthermore, leveraging experimental poroelastic data, this study investigates the effects of solid matrix compressibility on fluid pressure, porosity changes, and skeleton stress during undrained, transient, and drained states, highlighting the advantages of the analytical-based approach.